This invention relates to plates (referred to herein as “heave” plates or “damping” plates) attached to the submerged end of a spar (or column), where the plates are shaped to increase the effective mass of the spar and to affect the phase relationship of vertical motion of the spar.
There are many applications where it is desirable to control the (up down) movement of an element placed in a body of water and subjected to the forces of the waves.
For example, in the case of wave energy converters (WECs), the system includes a buoy having a relatively flat float (hereinafter the “float”) and an elongated float (hereinafter the “spar”) which, when placed in a body of water, can move relative to each other in response to the motion of the waves. The WEC includes a power take off device (PTO) responsive to the relative motion between the spar and the float for producing suitable forms of energy, mechanical and/or electrical. In the case of the WEC, to improve the efficiency of power production, it is desired that the flat float move up and down generally in phase with the waves in the body of water in which the WEC is placed. However, it is desired that the spar move out of phase with respect to the waves and the float. This may be effectuated by attaching a heave (damping) plate to the submerged portion of the spar.
The heave plate is disposed in a plane which is generally transverse (perpendicular) to the up or down direction of motion of the spar for increasing the effective mass of the spar. A plate so attached affects the dynamic behavior of the spar by increasing the effective mass and the viscous drag in the heave (vertical) direction. In general, the benefit of attaching one, or more, heave plates is to allow for a shorter vertical spar that will still have a heave natural period outside of the prevailing wave period for the operating conditions (so that the spar will not respond to the prevailing wave conditions) and to increase the viscous damping of the spar in order to decrease near-resonance responses. The heave plates that have been employed in the past include thin square, circular, or rectangular plates that are either solid or have holes punched in them.
The added mass that the heave plates contribute is due to the fact that the acceleration or deceleration of the plate requires movement of some volume of fluid around the plate as it moves. The volume of fluid that the plate will move is proportional to the equivalent volume of the plate times some (experimentally determined) factor.
The equivalent volume of the plate depends upon the geometry of the plate, however the general rule is that the equivalent volume is the area of the plate multiplied by a linear dimension of the plate; e.g., the radius of a circular plate, the side length of a square plate; the width of a rectangular plate, etc. By way of example, the equivalent volume of a square plate of width and length d is a cube (d3), that of a circular plate of radius r is a sphere (4/3πr3), and that of a rectangular plate of length L and width d is a cuboid (3-D rectangle) by using the shorter dimension, d, as the 3rd multiplier (Ld2). In general heave plates are made thin to save on cost and weight; however a heave plate may be made to have an appreciable thickness to provide needed structural strength, or to use as a buoyancy chamber. If the heave plate is made thick, then the added mass may be modeled in a similar fashion to that described above. Also, although not discussed, the volume of fluid moved is also a function of the frequency with which the plate is moving.
The accelerated flow inertia force caused by the heave plate is the added mass of the system (the density of water times the equivalent volume times the experimental factor) times the acceleration of the system, or:FInterial=(CmVequivalentρ)a=AddedMass*a,  Equation 1where Cm is the experimentally determined factor Vequivalent is the equivalent volume defined above, p is the density of water, and a is the acceleration. Note that the added mass term, with units of mass, is the combination of the variable inside of the parenthesis.
In general, heave plates are placed between one length scale (d if a square or rectangle, r if a circle) below the surface of the water and one length scale above the ocean floor so that the full equivalent volume of fluid may be captured. For optimal heave plate operation, the heave plate is placed with as deep a draft as possible in order to reduce the effect of wave exciting forces.
It is advantageous to use heave plates to increase the effective mass (or hydrodynamic inertia) of a spar and to move the natural period of the spar outside of prevailing wave conditions. As shown in FIGS. 1A and 1B, the concept of using a heave plate to dampen the up down movement and to move heave natural resonance period outside of operational conditions is employed in association with offshore structures such as platforms 991 used in the offshore oil industry (like the truss spar or cell spar) as it yields a low cost/high benefit solution to the large dynamic range of the ocean. In the case of the oil platforms, a central spar (or column) is, or multi-columns are, fixedly attached to a platform to stabilize the platform and reduce its vertical motion. A heave (or damping) plate may be attached to the submerged portion of the spar to increase its effective hydrodynamic mass and introduce damping at near resonance events. The use of heave (or damping) plates enables the length of the spar to be reduced by creating a heave natural period that is outside of the prevailing wave periods in the operational climate.
The use of heave plates provides the advantages discussed above. However, in accordance with the prior art, the only known way to increase the effective mass of a spar via the use of heave (damping) plates (in order to increase the heave natural resonance period of the spar) is to increase the length scale (d, r, or L as mentioned above) of the heave plates (which is equivalent to increasing the surface area of the heave plates) or to increase the number of plates present. An increase in length scale can be hard to achieve when considerations of harbor depth, structural strength along the dimension of increase, and weight of the plate are taken into account. An increase in the number of plates requires the use of a longer supporting spar structure.
Thus, although the use of known heave plates presents significant advantages, it is desirable to further increase the effective mass of a spar-like structure without increasing the size of the spar and/or the length scale of the heave plate.